MultipoleMultipole Quenching Cross Section for Collision between ExcitedAtoms and MoleculesYingNan Chiu Citation: The Journal of Chemical Physics 56, 5741 (1972); doi: 10.1063/1.1677107 View online: http://dx.doi.org/10.1063/1.1677107 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/56/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Excitation cross sections for electron collisions with sulfur atoms J. Chem. Phys. 92, 2374 (1990); 10.1063/1.457979 Quenching cross sections of neon metastable atoms by light molecules J. Appl. Phys. 66, 4010 (1989); 10.1063/1.344009 Cross sections for excitation of the potassium resonance doublet in collisions between potassiumatoms and alkali ions J. Chem. Phys. 65, 5518 (1976); 10.1063/1.433009 Quenching cross sections for electronic energy transfer reactions between metastable argon atoms andnoble gases and small molecules J. Chem. Phys. 59, 3323 (1973); 10.1063/1.1680477 Semiclassical Approximation for the Total Cross Section of Atom–DiatomicMolecule Collisions;Quenching of Glory Undulations J. Chem. Phys. 50, 3124 (1969); 10.1063/1.1671523

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LETTERS TO THE EDITOR 5741

In fact, any arbitrary cell potential can be used to calculate the partition function of a polymer and previous approximations, although useful, are un­necessary.

I!. Prigogine, N. Trappeniers and V. Mathot, Discussions Faraday Soc. 15, 93 (1953).

2 1. Prigogine, The Molecular Theory of Solutions (Interscience, New York, 1957).

3 V. Nanda and R. Simha, J. Chern. Phys. 41, 1884 (1964). • V. Nanda and R. Simha, J. Chern. Phys. 41, 3870 (1964). 5 J. G. Kirkwood, J. Chern. Phys. 18,380 (1950).

* This work supported by the U.S. Atomic Energy Com­mission (SC-DC-714527).

6 J. Barker, Lattice Theories of the Liquid State (Pergamon, New York, 1963).

THE JOURNAL OF CHEMICAL PHYSICS VOLUME 56, NUMBER II I JUNE 1972

Multipole-Multipole Quenching Cross Section for Collision between Excited Atoms and Molecules*

YING-NAN Cmut Department of Chemistry, The Catholic University of America, Washington, D. C. 20017

(Received 10 February 1972)

In a workl on collisional transfer of rovibronic and translational energy, we have derived the differential and total cross sections for the collision between two diatomic molecules. In this note we generalize the results to the (fluorescence-) quenching collision between an atom (A) and a diatomic molecule (XY) , again assuming the multipole-multipole interaction mechanism.

The collision reaction is

(1)

where A and A are the electronic angular momenta of the diatomic molecule (denoted by subscript a); v is the vi­brational quantum number; s, 1, and Jb are the angular momenta in I-s coupling and J representation of the atom (denoted by subscript b). The initial (i) and final (f) states of this reaction may be represented as:

I i)=L iL [47r(2L+l) Jl /2(kR)-1 L L C(JJJab; Ma, Mb, Mab)C(JabLf; Mab, 0, M) L hb J

x I AaxaAn 23·t11J.kJJJa~M), (2a)

I f)= L iL/[47r(2L'+ 1) JlI2(k'R)-1 L DML'OL/(nk') L L C(Ja'Jb'Jab'; Ma', Mb', Mab')C(Jab'L'J'; Mab'M L', M') L/ ML' Jab' J,

x I Aa'Xln'281+11Jb/k'Ja'Jb'Jab'L'JM), (2b)

where L is the relative motional angular momentum, k comes from relative kinetic energy, and R is the relative coordinate. Xa is the vibrational wavefunction of the diatomic molecule and J is the total angular momentum. Other symbols were explained in Paper I. Following the same arguments in Paper I, we obtained the total cross section for collisional quenching as

(1'= (2J.L/fi2)2(k3k')-I47r(2Ja+1)-1(2Jb+1)-1(2Ja'+1) (2N+l) {(2Ia+21b) !j[(21a+l) !(2Ib+l) !JI X L L L: (2L'+ 1) / (AaJa' 1/ L: erio.1aTla(ri) 1/ AJa) 12 / (2.'+IIJ./Jb/ 1/ L erj/,zbTz. (rj) l/23+l[J.Jb) /2

doubling L/ L i j

X / (k'L' 1/ T I.+I.(l1)R-la-Ib-SI/ kL) /2 [Sn'n>.A]= (2J.L/fi2) 2k--2'11'1 (2Ja+ 1)-1 (2h+ 1)-1

X {(2Ia+21b) !j[(2Ia+l) !(2Ib+l) !J} L: L: L: (2L+l)S>'.'rA.(Ja~Ja')SI'f-..z(h~N)C2(L, la+lb, L'; (00) doubling L/ L

where J.L is the reduced mass of the system, la, Ib come from 21a pole and 21b pole interaction, Sn'n>.A is the Franck­Condon overlap integral and S~A and Sl''r l are line strengths ofthe multipole transition. The reduced multipole

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5742 LETTERS TO THE EDITOR

matrix element for an atomic transition is

X (R(2B1+11.r./) IlL er;'l>'b II R(28+l1J,»= (2Jb+1/2N+1)1/2C(JJb-h'j 000) J R(28'+lIJ,/) erblhR (2B+lIJb) rb2drb, (4) j

where R(28+ll"b), equal to R(nl) /r in the hydrogenic atom,2 is the radial wavefunction of the atom. This reduced matrix element is related to the lifetime (r) and Einstein's coefficient (A) for spontaneous (multipole) emlSSlOn of the atomic state as:

r-1= A Jb"''''' (2 Ib -pole) = 47r(h+ 1) (21rp )2lb+ISI'f-I(h-~N) /hh(2h+ 1) [(2h-1) ! !]2C2lb+1(2Jb+ 1)

= [47r(h+ 1) (21rp )2lb+1(2N+ 1) /hlb(2Ib+ 1) [(2Ib-1) ! !]C2lb+1(2Jb+ 1) ] I (28'+llJ,/N II erlTl 112s+IIJbJb) 12. (5)

The corresponding matrix elements for the diatomic molecule have been given in Paper I. For dipole-dipole interaction t. = h= 1, the total cross section is

u=i(2J.L/Ii,2)2k-2 L L L T(2L+1) (2Ja+1)-1(2Jb+1)-IS4-A(Ja--~Ja')Sl'f-I(h-~N)C2(L, 2, L'j (00) doubling L L'

x [Sn'nU]2 [{a h'+1/2(k'R)h+1/2(kR)/R2dR r (6)

For the 6 ISo-6 3PI transition of-the mercury atom, if we take the lifetime3 r= 1.08 X 10-7 sec, then from Eq. (5):

1/r= AlJ.+l (2-pole) = (647rY /3c3h) S(1So~3PI)

= (647r'P3/3c3h)C2(01l, (00) (R(3Pl) I er I R(1S0»2

(7)

The transition moment M(1So-3Pl) may be estimated to be 0.694 D. Similarly, the line strength and transition momentl etc., for the diatomic molecule can be obtained from experimental lifetime or oscillator strengths.

The writer wishes to thank Dr. Jon T. Hougen of the National Bureau of Standards for hospitality.

* Work supported in part by the National Science Foundation (GP 11212).

t Alfred P. Sloan Research Fellow on sabbatical leave at the National Bureau of Standards (15 November-IS December, 1971) .

1 Y.-N. Chiu, J. Chem. Phys. 55, 5052 (1971). Hereafter referred

Comments

THE JOURNAl, OF CHEMICAL PHYSICS

to as Paper I. 2 E. U. Condon and G. H. Shortley, The Theory of Atomic

SPectra (Cambridge U. P., Cambridge, England, 1953). 'A. C. G. Mitchell and M. W. Zemansky, Resonance Radia­

tion and Excited A/OlliS (Cambridge U. P., Cambridge, England 1961) p. 147.

VOLUME 56, NUMBER II I JUNE 1972

Comments on Molecular Nonradiative Transition Probabilities in the Statistical Limit

JOSHUA JORTNER

Department oj Chemistry, Tel-Aviv University, Tel-Aviv, Israel

(Received 4 October 1971)

Nonradiative molecular decay in the statistical limitl-6 can be considered as multiphonon process,7-IO the thermally averaged transition probability (W) being expressed as a weighted density of states func­tion9-11

(W)= L p(Si)W.i,

where

W8i= L I V. i •l; 12 o (E.i-Elj) ;

is represented by a Fourier transform of a generating function which can be recast in terms of Green's func­tions for nuclear motion7- lO while W.; can be expressed

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